• JackbyDev@programming.dev
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      18 days ago

      Now that’s a good troll math thing because it gets really deep into the weeds of mathematical notation. There isn’t one true order of operations that is objectively correct, and on top of that, that’s hardly the way most people would write that. As in, if you wrote that by hand, you wouldn’t use the / symbol. You’d either use ÷ or a proper fraction.

      It’s a good candidate for nerd sniping.

      Personally, I’d call that 36 as written given the context you’re saying it in, instead of calling it 1. But I’d say it’s ambiguous and you should notate in a way to avoid ambiguities. Especially if you’re in the camp of multiplication like a(b) being different from ab and/or a × b.

      • There isn’t one true order of operations that is objectively correct

        Yes there is, as found in Maths textbooks the world over

        that’s hardly the way most people would write that

        Maths textbooks write it that way

        you wouldn’t use the / symbol

        Yes you would.

        You’d either use ÷

        Same same

        It’s a good candidate for nerd sniping.

        Here’s one I prepared earlier to save you the trouble

        I’d call that 36

        And you’d be wrong

        as written given the context you’re saying it in

        The context is Maths, you have to obey the rules of Maths. a(b+c)=(ab+ac), 5(8-5)=(5x8-5x5).

        But I’d say it’s ambiguous

        And you’d be wrong about that too

        you should notate in a way to avoid ambiguities

        It already is notated in a way that avoids all ambiguities!

        Especially if you’re in the camp of multiplication like a(b)

        That’s not Multiplication, it’s Distribution, a(b+c)=(ab+ac), a(b)=(axb).

        being different from ab

        Nope, that’s exactly the same, ab=(axb) by definition

        and/or a × b

        (axb) is most certainly different to axb. 1/ab=1/(axb), 1/axb=b/a

        • JackbyDev@programming.dev
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          1 day ago

          Please read this section of Wikipedia which talks about these topics better than I could. It shows that there is ambiguity in the order of operations and that for especially niche cases there is not a universally accepted order of operations when dealing with mixed division and multiplication. It addresses everything you’ve mentioned.

          https://en.wikipedia.org/wiki/Order_of_operations#Mixed_division_and_multiplication

          There is no universal convention for interpreting an expression containing both division denoted by ‘÷’ and multiplication denoted by ‘×’. Proposed conventions include assigning the operations equal precedence and evaluating them from left to right, or equivalently treating division as multiplication by the reciprocal and then evaluating in any order;[10] evaluating all multiplications first followed by divisions from left to right; or eschewing such expressions and instead always disambiguating them by explicit parentheses.[11]

          Beyond primary education, the symbol ‘÷’ for division is seldom used, but is replaced by the use of algebraic fractions,[12] typically written vertically with the numerator stacked above the denominator – which makes grouping explicit and unambiguous – but sometimes written inline using the slash or solidus symbol ‘/’.[13]

          Multiplication denoted by juxtaposition (also known as implied multiplication) creates a visual unit and is often given higher precedence than most other operations. In academic literature, when inline fractions are combined with implied multiplication without explicit parentheses, the multiplication is conventionally interpreted as having higher precedence than division, so that e.g. 1 / 2n is interpreted to mean 1 / (2 · n) rather than (1 / 2) · n.[2][10][14][15] For instance, the manuscript submission instructions for the Physical Review journals directly state that multiplication has precedence over division,[16] and this is also the convention observed in physics textbooks such as the Course of Theoretical Physics by Landau and Lifshitz[c] and mathematics textbooks such as Concrete Mathematics by Graham, Knuth, and Patashnik.[17] However, some authors recommend against expressions such as a / bc, preferring the explicit use of parenthesis a / (bc).[3]

          More complicated cases are more ambiguous. For instance, the notation 1 / 2π(a + b) could plausibly mean either 1 / [2π · (a + b)] or [1 / (2π)] · (a + b).[18] Sometimes interpretation depends on context. The Physical Review submission instructions recommend against expressions of the form a / b / c; more explicit expressions (a / b) / c or a / (b / c) are unambiguous.[16]

          Image of two calculators getting different answers 6÷2(1+2) is interpreted as 6÷(2×(1+2)) by a fx-82MS (upper), and (6÷2)×(1+2) by a TI-83 Plus calculator (lower), respectively.

          This ambiguity has been the subject of Internet memes such as “8 ÷ 2(2 + 2)”, for which there are two conflicting interpretations: 8 ÷ [2 · (2 + 2)] = 1 and (8 ÷ 2) · (2 + 2) = 16.[15][19] Mathematics education researcher Hung-Hsi Wu points out that “one never gets a computation of this type in real life”, and calls such contrived examples “a kind of Gotcha! parlor game designed to trap an unsuspecting person by phrasing it in terms of a set of unreasonably convoluted rules”.[12]

          • Please read this section of Wikipedia which talks about these topics better than I could

            Please read Maths textbooks which explain it better than Joe Blow Your next Door neighbour on Wikipedia. there’s plenty in here

            It shows that there is ambiguity in the order of operations

            and is wrong about that, as proven by Maths textbooks

            especially niche cases there is not a universally accepted order of operations when dealing with mixed division and multiplication

            That’s because Multiplication and Division can be done in any order

            It addresses everything you’ve mentioned

            wrongly, as per Maths textbooks

            Multiplication denoted by juxtaposition (also known as implied multiplication)

            Nope. Terms/Products is what they are called. “implied multiplication” is a “rule” made up by people who have forgotten the actual rules.

            s often given higher precedence than most other operations

            Always is, because brackets first. ab=(axb) by definition

            1 / 2n is interpreted to mean 1 / (2 · n)

            As per the definition that ab=(axb), 1/2n=1/(2xn).

            [2][10][14][15]

            Did you look at the references, and note that there are no Maths textbooks listed?

            the manuscript submission instructions for the Physical Review journals

            Which isn’t a Maths textbook

            the convention observed in physics textbooks

            Also not Maths textbooks

            mathematics textbooks such as Concrete Mathematics by Graham, Knuth, and Patashnik

            Actually that is a Computer Science textbook, written for programmers. Knuth is a very famous programmer

            More complicated cases are more ambiguous

            None of them are ambiguous.

            the notation 1 / 2π(a + b) could plausibly mean either 1 / [2π · (a + b)]

            It does as per the rules of Maths, but more precisely it actually means 1 / (2πa + 2πb)

            or [1 / (2π)] · (a + b).[18]

            No, it can’t mean that unless it was written (1 / 2π)(a + b), which it wasn’t

            Sometimes interpretation depends on context

            Nope, never

            more explicit expressions (a / b) / c or a / (b / c) are unambiguous

            a/b/c is already unambiguous - left to right. 🙄

            Image of two calculators getting different answers

            With the exception of Texas Instruments, all the other calculator manufacturers have gone back to doing it correctly, and Sharp have always done it correctly.

            6÷2(1+2) is interpreted as 6÷(2×(1+2))

            6÷(2x1+2x2) actually, as per The Distributive Law, a(b+c)=(ab+ac)

            (6÷2)×(1+2) by a TI-83 Plus calculator (lower)

            Yep, Texas Instruments is the only one still doing it wrong

            This ambiguity

            doesn’t exist, as per Maths textbooks

            “8 ÷ 2(2 + 2)”, for which there are two conflicting interpretations:

            No there isn’t - you MUST obey The Distributive Law, a(b+c)=(ab+ac)

            Mathematics education researcher Hung-Hsi Wu points out that “one never gets a computation of this type in real life”

            And he was wrong about that. 🙄

            calls such contrived examples

            Which notably can be found in Maths textbooks

            • JackbyDev@programming.dev
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              1 day ago

              If you believe the article is incorrect, submit your corrections to Wikipedia instead of telling me.

              • If you believe the article is incorrect, submit your corrections to Wikipedia

                You know they’ve rejected corrections by actual Maths Professors right? Just look for Rick Norwood in the talk section. Everyone who knows Maths knows Wikipedia is wrong, and looks in the right place to begin with - Maths textbooks

    • MotoAsh@piefed.social
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      18 days ago

      Well, now you might be running into syntax issues instead of PEMDAS issues depending on what they’re confused about. If it’s 12 over 2*6, it’s 1. If it’s 12 ÷ 2 x 6, it’s 36.

      A lot of people try a bunch of funky stuff to represent fractions in text form (like mixing spaces and no spaces) when they should just be treating it like a programmer has to, and use parenthesis if it’s a complex fraction in basic text form.

    • Feathercrown@lemmy.world
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      18 days ago

      The P in PEMDAS means to solve everything within parentheses first; there is no “distribution” step or rule that says multiplying without a visible operator other than parentheses comes first. So yes, 36 is valid here. It’s mostly because PEMDAS never shows up in the same context as this sort of multiplication or large fractions

      • The P in PEMDAS means to solve everything within parentheses first

        and without a(b+c)=(ab+ac), now solve (ab+ac)

        there is no “distribution” step or rule

        It’s a LAW of Maths actually, The Distributive Law.

        that says multiplying without a visible operator

        It’s not “Multiplying”, it’s Distributing, a(b+c)=(ab+ac)

        So yes, 36 is valid here

        No it isn’t. To get 36 you have disobeyed The Distributive Law, thus it is a wrong answer

        It’s mostly because

        people like you try to gaslight others that there’s no such thing as The Distributive Law

        • Feathercrown@lemmy.world
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          20 hours ago

          Are you under the impression that atomizing your opponents statements and making a comment about each part individually without addressing the actual point (how those facts fit together) is a good debate tactic? Because it seems like all you’ve done is confuse yourself about what I was saying and make arguments that don’t address it. Never mind that some of those micro-rebuttals aren’t even correct.

          • addressing the actual point (how those facts fit together)

            I did address the actual point - see Maths textbooks

            all you’ve done is confuse yourself

            I’m not confused at all. I’m the one who knows the difference between Distribution and Multiplication.

            what I was saying

            You lied about there being no such thing as “the Distribution step” (Brackets), proven wrong by the textbooks

            make arguments that don’t address it.

            Textbooks talking about The Distributive Law totally addresses your lie that no such step exists.

            Never mind that some of those micro-rebuttals aren’t even correct

            You think Maths textbooks aren’t correct?? 😂

            • Feathercrown@lemmy.world
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              9 hours ago

              I have said why this style of debate is bad in greater detail here: https://lemmy.world/post/39377635/21030374

              But to make a pointless effort to address your actual point, yes distribution exists, no it is not a step in PE(MD)(AS). Again, you have not understood my point because you categorically fail to engage with any argument. I don’t think you even understand what it means to do so. I will not respond further to either thread.